A thief is stopped by a policeman from a distance of 500 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 10 km/h and that of police man as 18 km/h, how far the thief would have run, before he is over - taken?

A thief is stopped by a policeman from a distance of 500 metres. When the policeman starts the chase, the thief also starts running. Assuming the speed of the thief as 10 km/h and that of police man as 18 km/h, how far the thief would have run, before he is over - taken? Correct Answer 625 metre

Given:

A thief is stopped by a policeman from a distance of 500 metres.

When the policeman starts the chase, the thief also starts running.

The speed of the thief as 10 km/h and that of police man as 18 km/h.

Concept used:

Time = Distance/speed

When two bodies moving in the same direction then the relative speed of them will be difference of the individual speed

Calculation:

Speed of the thief = 10 km/hr = 10 × 5/18 = 25/9 m/s

Speed of the police = 18 km/hr = 18 × 5/18 = 5 m/s

Also given that thief is stopped by a policeman from a distance of 500 metres

Let x be the distance covered by the thief, then distance covered by police = x + 500 m

We know speed = distance /time

⇒ (500 + x)/5 = x/(25/9)

⇒ (500 + x)/5 = 9x/25

⇒ (500 + x) = 9x/5

⇒ 2500 + 5x = 9x

⇒ 4x = 2500

⇒ x = 625 m